where \(g_{\alpha \beta }=g_{MN}\partial _\alpha x^M\partial _\beta x^N \ , \quad B_{\alpha \beta }=B_{MN}\partial _\alpha x^M\partial _\beta x^N\)  and where \(\epsilon ^{01}=1=-\epsilon _{01}\)  and \(T_F\)  is string tension.
As in
[1]} we introduce
indices \(\underline{a}=(A,a)\)  corresponding to directions longitudinal and transverse to
string world-sheet where \(A=0,1\)  are longitudinal and \(a=2,\dots ,9\)  are transverse.
Then we have
\(e_M^{ \ \underline{a}}=(cE_M^{ \ A},e_M^{ \ a}) \ , \quad \pi _M^{ \ \underline{a}}=(c\Pi _M^{ \ A},\pi _M^{ \ a}) \ \) 
